Fixed Point Homing Shuffles
We study a family of maps from $S_n \to S_n$ we call fixed point homing shuffles. These maps generalize a few known problems such as Conway's Topswops, and a card shuffling process studied by Gweneth McKinley. We show that the iterates of these homing shuffles always converge, and characterize...
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| Published in: | Discrete mathematics and theoretical computer science Vol. 27:1, Permutation...; no. Special issues |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
18.08.2025
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| Subjects: | |
| ISSN: | 1365-8050, 1365-8050 |
| Online Access: | Get full text |
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| Summary: | We study a family of maps from $S_n \to S_n$ we call fixed point homing shuffles. These maps generalize a few known problems such as Conway's Topswops, and a card shuffling process studied by Gweneth McKinley. We show that the iterates of these homing shuffles always converge, and characterize the set $U_n$ of permutations that no homing shuffle sorts. We also study a homing shuffle that sorts anything not in $U_n$, and find how many iterations it takes to converge in the worst case.
Updated formatting to fit with DMTCS requirements |
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| ISSN: | 1365-8050 1365-8050 |
| DOI: | 10.46298/dmtcs.14653 |